Nonlinear Response of an Oscillator with a Magneto-Rheological Damper Subjected to External Forcing

Abstract:

Article Preview

This paper examines the dynamics of a single degree of freedom nonlinear model,
representing a quarter of an automobile with a semi-active, nonlinear suspension. Assuming that
the kinematic excitation caused by the road surface profile is harmonic, the principal resonance
and frequency entrainment are obtained for regions of the model parameters. Changing the
excitation frequency and road profile amplitude we analyze possible chaotic vibrations and
bifurcations of the system.

Abstract: The recovery force of shape memory alloy spring is described by using polynomial constitutive equation. The nonlinear dynamic model of forced vibration for the shape memory alloy spring oscillator is derived. Numerical simulations are performed by a fourth-order Runge-Kutta method. The bifurcation diagram and Lyapunov-exponent spectrum are presented while the dimensionless temperature, the dimensionless damping coefficient or the dimensionless amplitude of exciting force is varied respectively, thus the bifurcation of the system is investigated. Furthermore, the periodic and chaotic motions of the system are analyzed by means of the displacement time history diagram, the phase portrait, the Poincare section diagram and the power spectrum with different parameters. The results show that the periodic or chaotic motion of the system occur by changing temperature, damping coefficient and amplitude of exciting force, thus the vibration of the system could be controlled.

Abstract: One dynamical model of a thin rectangular plate subject to in-plate parametrical excitation is proposed based on elastic theory and Galerkin’s approach. At first, the undermined fundamental frequency and normal form method was utilized to study the influence of the disturbing parameters to the fundamental frequency. Secondly, the improved Melnikov expression for the oscillator was built based on the results of the undermined fundamental frequency method and time scale transformation to improve the approximate threshold value of chaotic motion in the Homoclinicity. Finally, the numerical results show the efficiency of the theoretical analysis.

Abstract: The nonlinear dynamics equation of passive vibration isolator is established in this paper. According to the nonlinear vibration theory, the average equation of slow-varying primary harmonic in the condition of weak nonlinearity is abstained , and derived a discrete mapping of the harmonic slow variable parameter state equation, then get the analytical conditions of chaos in the passive vibration isolator, the analytical results show that only when the vibration frequency of the groundsill is higher than the inherent frequency of the passive vibration isolator, the chaos can be observed, when the groundsill vibrate with the large amplitude and high frequency vibration, the chaos can’t be observed in the passive vibration isolator system. Finally the analytical prediction is validated by analog simulation experiment, and gets the conclusion that the prediction matches well with the simulation results.

Abstract: In this paper, in order to study the effect of nonlinear suspension system, a nonlinear dynamic model considering nonlinearity of suspension is built and another model with the respective of linear suspension system is developed which is for comparison. Then the dynamic equation of the model is set up. The simulation is accomplished through MATLAB/SIMULINK. It is found that the band-limited white noise module can simulate the power spectral density of road surface well. Finally, numerical simulation results indicates that an appropriate nonlinear suspension model fits reality better than a linear one and using relative control can provide the best ride comfort.

Abstract: The harvesting of ambient energy has become more important over the last years. This paper will investigate an analytical effort to predict the Duffing parameters for a magnetoelastic cantilever structure. The modeling is compared to a nonlinear harvester with point dipoles. The system consists of a harmonic excited cantilever structure with a magnetic tip mass. The beam is firmly clamped to the host structure. A second oppositely poled permanent magnet is located near the free end of the beam. The system is a bistable nonlinear oscillator with two equilibrium positions. Several studies show the better performance of the setup. The approach is not limited for energy harvesting techniques. The setup is suitable for broadband oscillations and also to tune the resonant frequency closer to the excitation frequency.